Cascade model for fluvial geomorphology

Abstract

Erosional landscapes are generally scale invariant and fractal. Spectral studies provide quantitative confirmation of this statement. Linear theories of erosion will not generate scale‐invariant topography. In order to explain the fractal behaviour of landscapes we have introduced a modified Fourier series that is the basis for a renormalization approach. We have introduced a non‐linear dynamical model for the decay of the modified Fourier series coefficients that yield a fractal spectra. We argue that a physical basis for our approach is that a fractal (or nearly fractal) distribution of storms (floods) continually renews erosional features on all scales. Copyright © 1990, Wiley Blackwell. All rights reserved